Finite Group Databasebeta

← #11864090

Subgroups — #11864090

Order 1152.

1597 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×#63948C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4#10594627C211yesmaximal, characteristic, complemented
5#10592509C211yesmaximal, characteristic, complemented
6C3×#4808C211yesmaximal, characteristic, complemented
7C3×#4802C211yesmaximal, characteristic, complemented
8#10591602C211yesmaximal, characteristic, complemented
9#10591588C211yesmaximal, characteristic, complemented
10#10590967C211yesmaximal, characteristic, complemented
11#10590961C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590617C211yesmaximal, characteristic, complemented
14#10590616C211yesmaximal, characteristic, complemented
15#10590592C211yesmaximal, characteristic, complemented
16#80227—31nomaximal
17#78959—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21D3×#239—24no—
22D3×#239—24no—
23C2×D3×D12—21no—
24C2×D3×D12C2211yescharacteristic
25C2×C4×D32—21no—
26C2×C4×D32C2211yescharacteristic
27C2×#3799—21no—
28C2×#3799C2211yescharacteristic
29C2×#3799C2211yescharacteristic
30C2×#3796—21no—
31C2×#3796C2211yescharacteristic
32C2×#3755C2211yescharacteristic, complemented
33C2×#3745C2211yescharacteristic, complemented
34#64104C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
38C3×#897C2211yescharacteristic, complemented
39C3×#892C2211yescharacteristic
40#63948—24no—
41#63923—21no—
42#63909C2211yescharacteristic, complemented
43#63894—21no—
44#63890—21no—
45#63880—21no—
46#63871C2211yescharacteristic, complemented
47C2×#3718C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic
52#63794—24no—
53C32×#103C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#239—31no—
67C2×#942—31no—
68C2×#918—31no—
69C2×#914—31no—
70C2×#908—31no—
71#5627—31no—
72#5524—31no—
73C3×#452—31no—
74C3×#419—31no—
75#5238—31no—
76#5187—31no—
77#5173—31no—
78#5126—31no—
79#5047—31no—
80#5001—31no—
81#4810—31no—
82#4810—31no—
83#4810—31no—
84#4810—31no—
85#4810—31no—
86#4810—61no—
87#4808—31no—
88#4808—31no—
89#4808—31no—
90#4808D311yescharacteristic, complemented
91#4802D311yescharacteristic, complemented
92#4781—31no—
93#4770—31no—
94#4734—31no—
95#4726—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99#3832—22no—
100#3832—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C3×#239—22no—
108C3×#239—22no—
109C3×D3×Q8—22no—
110C3×D3×Q8D414yescomplemented
111C2×C3×D12—21no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#626—21no—
125C2×#624—21no—
126C2×#624—21no—
127C2×#624D411yescharacteristic
128C2×D3×Dic3—21no—
129C2×D3×Dic3D411yescharacteristic
130C2×D3×Dic3D411yescharacteristic
131D3×D12—28no—
132D3×D12—22no—
133D3×D12D414yescomplemented
134C4×D32—28no—
135C4×D32—22no—
136C4×D32—22no—
137#3799—28no—
138#3799—22no—
139#3799—22no—
140#3799—22no—
141#3799—22no—
142#3796—28no—
143#3796—22no—
144#3796—22no—
145C2×C32×C8C2311yescharacteristic
146C32×C4⋊C4C2311yescharacteristic
147#3755—22no—
148#3752—21no—
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150#3745—22no—
151C3×#216—22no—
152C3×(C2×D3)⋊C4—21no—
153C3×(C2×D3)⋊C4—21no—
154C3×C4⋊Dic3—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4×Dic3—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×#204—22no—
160C3×ΓL(1,𝔽25)—22no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163#3722—21no—
164#3718—22no—
165#3717—22no—
166#3717—22no—
167#3714—22no—
168#3711—22no—
169#3005—91noSylow
170C2×C3×#41—31no—
171C22×C3×Q8—31no—
172D3×#41—64no—
173D3×#41—64no—
174C2×#239—31no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—61no—
180C2×#239—61no—
181C2×#239—61no—
182C2×#239—64no—
183C2×#239—64no—
184C2×#239C2×D311yescharacteristic
185C2×D3×Q8C2×D311yescharacteristic
186C2×#237—31no—
187C2×#237—61no—
188C2×D3×D4—31no—
189C2×D3×D4—61no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—61no—
193C22×D12—31no—
194C22×D12—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×C4×D3—61no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C2×C3×M16—31no—
202C3×C22⋊Q8—31no—
203C3×#117—31no—
204#946—31no—
205C2×#216—31no—
206C2×#216—31no—
207C2×#216C2×D311yescharacteristic, complemented
208#942—64no—
209C2×#215—31no—
210C2×#215—31no—
211C2×#215—31no—
212C2×#215—31no—
213C2×#215—61no—
214C2×#213—31no—
215#930—31no—
216C2×#208—31no—
217#918—64no—
218#914—64no—
219#908—64no—
220C2×D24—31no—
221C2×D24—31no—
222C2×D24—31no—
223C2×D24—61no—
224C2×#204—31no—
225C2×#204—31no—
226C2×#204C2×D311yescharacteristic, complemented
227C2×ΓL(1,𝔽25)—31no—
228C2×ΓL(1,𝔽25)C2×D311yescharacteristic
229#897—31no—
230#897C2×D311yescharacteristic, complemented
231#895—31no—
232#895—31no—
233#895—31no—
234#895—61no—
235#894—61no—
236#893—61no—
237#892C2×D311yescharacteristic
238#886—61no—
239#882—61no—
240#882—61no—
241#67⋊C4—61no—
242C4×D12—61no—
243C4×D12—61no—
244C3×#103—21no—
245C3×#103—31no—
246C3×#103—31no—
247C3×#103—31no—
248C3×#103C2×D311yescharacteristic, complemented
249C3×#103C2×D311yescharacteristic, complemented
250C3×#102—31no—
251C3×C22⋊C8—31no—
252#835C2×D311yescharacteristic, complemented
253#832—31no—
254#830—31no—
255#821—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—61no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816C2×D311yescharacteristic, complemented
264#810C2×D311yescharacteristic, complemented
265#809—31no—
266#809—31no—
267#809—31no—
268#809—31no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
271C22×C3⋊D3—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—21no—
275C22×C3×D3C2×D411yescharacteristic
276C22×C3×D3C2×D411yescharacteristic
277C2×D32—24no—
278C2×D32—22no—
279C2×D32—41no—
280C2×D32—41no—
281C2×D32—42no—
282C2×D32—42no—
283C32×Q8—21no—
284C32×Q8C2×D412yes—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4C2411yescharacteristic
288C2×C3⋊Dic3C2×D411yescharacteristic
289C4⋊(C3⋊D3)—24no—
290C4⋊(C3⋊D3)—21no—
291C4⋊(C3⋊D3)—21no—
292C4⋊(C3⋊D3)—21no—
293C4⋊(C3⋊D3)—42no—
294C4⋊(C3⋊D3)C2×D412yes—
295C4×C3⋊D3—24no—
296C4×C3⋊D3—21no—
297C4×C3⋊D3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3C2×D411yescharacteristic
302C2×C3×Dic3C2×D411yescharacteristic
303C3×D12—24no—
304C3×D12—21no—
305C3×D12C2×D412yes—
306C3×C4×D3—24no—
307C3×C4×D3—24no—
308C3×C4×D3—21no—
309C3×C4×D3—21no—
310C3×C4×D3C2×D412yes—
311C3×C4×D3C2×D412yes—
312C3×Dic6—21no—
313C3×Dic6—24no—
314C3×Dic6—21no—
315C3×Dic6—21no—
316C3×Dic6C2×D412yes—
317#626—24no—
318#626—24no—
319#626—24no—
320#626—42no—
321#626—42no—
322#624—24no—
323#624—22no—
324#624—42no—
325D3×Dic3—24no—
326D3×Dic3—22no—
327D3×Dic3—22no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—91no—
333C2×#137—91no—
334C2×AGL(1,ℤ/8)—91no—
335#525—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#449—91no—
341#449—91no—
342#449—91no—
343#449—91no—
344#419—31no—
345#418—91no—
346#407—91no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3—61no—
351C3×#41—62no—
352C3×#41—62no—
353C2×C3×Q8—21no—
354C2×C3×Q8—34no—
355C2×C3×Q8—31no—
356C2×C3×Q8—31no—
357C2×C3×Q8—61no—
358C2×C3×Q8—62no—
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×Q8C22×D311yescharacteristic
361C2×C3×D4—31no—
362C2×C3×D4—61no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—61no—
366C22×C3×C4—61no—
367C2×#67—61no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—61no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—61no—
375#239—22no—
376#239—22no—
377#239—62no—
378#239—62no—
379#239—68no—
380#239—62no—
381#239—68no—
382#239—62no—
383#239—62no—
384#239—62no—
385#239—62no—
386#239—62no—
387#239—62no—
388#239—62no—
389#239—122no—
390#239—122no—
391D3×Q8—22no—
392D3×Q8D1214yescomplemented
393#237—62no—
394#237—68no—
395#237—62no—
396D3×D4—34no—
397D3×D4—68no—
398D3×D4—62no—
399#235—62no—
400#235—68no—
401#235—62no—
402#235—62no—
403#235—62no—
404C2×D12—21no—
405C2×D12—31no—
406C2×D12—31no—
407C2×D12—34no—
408C2×D12—31no—
409C2×D12—31no—
410C2×D12—61no—
411C2×D12—61no—
412C2×D12—62no—
413C2×D12—68no—
414C2×D12—61no—
415C2×D12—61no—
416C2×D12—61no—
417C2×D12—61no—
418C2×D12—61no—
419C2×D12—61no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—121no—
424C2×D12—121no—
425C2×D12C22×D311yescharacteristic
426C2×C4×D3—21no—
427C2×C4×D3—21no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—61no—
435C2×C4×D3—62no—
436C2×C4×D3—62no—
437C2×C4×D3—68no—
438C2×C4×D3—68no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—62no—
445C2×C4×D3—62no—
446C2×C4×D3—61no—
447C2×C4×D3—61no—
448C2×C4×D3—121no—
449C2×C4×D3C22×D311yescharacteristic
450C2×C4×D3C22×D311yescharacteristic
451C2×Dic6—21no—
452C2×Dic6C22×D311yescharacteristic
453C2×Dic6C22×D311yescharacteristic
454C3×Q16—62no—
455C3×SD16—62no—
456C3×M16—62no—
457C2×C3×C8—21no—
458C2×C3×C8—31no—
459C2×C3×C8—31no—
460C2×C3×C8C22×D311yescharacteristic
461C2×C3×C8C22×D311yescharacteristic
462C3×C4⋊C4—21no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4—61no—
465C3×C4⋊C4C22×D311yescharacteristic
466C3×C4⋊C4C22×D311yescharacteristic
467C3×C22⋊C4—61no—
468C3×C22⋊C4—61no—
469C3×C42—61no—
470#216—22no—
471#216—62no—
472#216—62no—
473#215—62no—
474#215—62no—
475#215—62no—
476#215—62no—
477#215—122no—
478#213—62no—
479(C2×D3)⋊C4—21no—
480(C2×D3)⋊C4—21no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—121no—
488C4⋊Dic3—21no—
489C4⋊Dic3—61no—
490C4⋊Dic3C22×D311yescharacteristic
491Dic3⋊C4—61no—
492C4×Dic3—21no—
493#208—62no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—61no—
497C2×C3⋊C8C22×D311yescharacteristic
498C2×C3⋊C8C22×D311yescharacteristic
499D24—62no—
500D24—62no—
501D24—62no—
502D24—122no—
503#204—22no—
504#204—62no—
505#204—62no—
506ΓL(1,𝔽25)—22no—
507ΓL(1,𝔽25)—62no—
508C22×C32C22×D411yescharacteristic
509C2×C3⋊D3—21no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—41no—
514C2×C3⋊D3—41no—
515C2×C3⋊D3—41no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—22no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3#12012yes—
527D32—44no—
528D32—48no—
529C32×C4—22no—
530C32×C4—41no—
531C32×C4C22×D411yescharacteristic
532C32×C4C22×D411yescharacteristic
533C3⋊Dic3—21no—
534C3×Dic3—21no—
535C3×Dic3—22no—
536C3×Dic3—41no—
537C3×Dic3—41no—
538C3×Dic3#12012yes—
539C2×#41—31no—
540C2×#41—91no—
541C2×#41—91no—
542C2×#41—91no—
543C2×#41—91no—
544C2×#41—181no—
545C2×#41—181no—
546C2×#41—184no—
547C2×#41—184no—
548C22×Q8—31no—
549C22×D4—91no—
550C22×D4—181no—
551C23×C4—91no—
552C23×C4—181no—
553#137—184no—
554AGL(1,ℤ/8)—184no—
555C2×Q16—31no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—91no—
562C2×D8—91no—
563C2×M16—31no—
564C2×M16—91no—
565#123—181no—
566C22⋊Q8—31no—
567C22⋊Q8—91no—
568#121—91no—
569#121—91no—
570#120—181no—
571C4×D4—181no—
572C4×D4—181no—
573#117—31no—
574#103—31no—
575#103—31no—
576#103—31no—
577#103D3211yescharacteristic, complemented
578#102—31no—
579#102—91no—
580#102—91no—
581#102—91no—
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C23×C3—31no—
587C23×C3—31no—
588C23×C3—61no—
589C22×D3—21no—
590C22×D3—31no—
591C22×D3—31no—
592C22×D3—61no—
593C22×D3—64no—
594C22×D3—62no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—64no—
598C22×D3—62no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3—122no—
611C22×D3D3×D411yescharacteristic
612C22×D3D3×D411yescharacteristic
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—22no—
616C3×Q8—32no—
617C3×Q8—41no—
618C3×Q8—64no—
619C3×Q8—61no—
620C3×Q8—61no—
621C3×Q8—61no—
622C3×Q8C2×D1212yes—
623C3×Q8D3×D412yes—
624C3×D4—32no—
625C3×D4—64no—
626C3×D4—61no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—31no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—31no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—64no—
639C2×C3×C4—64no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647#67—64no—
648#67—64no—
649#67—64no—
650#67—122no—
651#67—122no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—31no—
656C2×Dic3—31no—
657C2×Dic3—61no—
658C2×Dic3—62no—
659C2×Dic3—64no—
660C2×Dic3—62no—
661C2×Dic3D3×D411yescharacteristic
662C2×Dic3D3×D411yescharacteristic
663D12—24no—
664D12—21no—
665D12—32no—
666D12—32no—
667D12—62no—
668D12—64no—
669D12—64no—
670D12—64no—
671D12—64no—
672D12—64no—
673D12—61no—
674D12—61no—
675D12—61no—
676D12—61no—
677D12—61no—
678D12—61no—
679D12—121no—
680D12—121no—
681D12—121no—
682D12—124no—
683D12—122no—
684D12—122no—
685D12—122no—
686D12—122no—
687D12—242no—
688D12D3×D412yes—
689C4×D3—24no—
690C4×D3—24no—
691C4×D3—21no—
692C4×D3—21no—
693C4×D3—62no—
694C4×D3—64no—
695C4×D3—64no—
696C4×D3—64no—
697C4×D3—64no—
698C4×D3—62no—
699C4×D3—64no—
700C4×D3—62no—
701C4×D3—61no—
702C4×D3—61no—
703C4×D3—61no—
704C4×D3—61no—
705C4×D3—62no—
706C4×D3—121no—
707C4×D3—121no—
708C4×D3—124no—
709C4×D3—122no—
710C4×D3—122no—
711C4×D3C2×D1212yes—
712C4×D3D3×D412yes—
713Dic6—21no—
714Dic6—24no—
715Dic6—21no—
716Dic6—21no—
717Dic6C2×D1212yes—
718C3×C8—21no—
719C3×C8—21no—
720C3×C8—41no—
721C3×C8—61no—
722C3×C8—61no—
723C3⋊C8—21no—
724C3⋊C8—21no—
725C3⋊C8—61no—
726C3⋊C8—61no—
727C3⋊C8—121no—
728C2×C32C2×#12011yescharacteristic
729C2×C32#57511yescharacteristic
730C2×C32#57511yescharacteristic
731C3⋊D3—41no—
732C3⋊D3—42no—
733C3⋊D3—81no—
734C3×D3—22no—
735C3×D3—41no—
736C3×D3—42no—
737C24—91no—
738C24—181no—
739#41—62no—
740#41—62no—
741#41—182no—
742#41—182no—
743#41—182no—
744#41—182no—
745#41—188no—
746#41—182no—
747#41—182no—
748#41—188no—
749#41—182no—
750#41—182no—
751C2×Q8—34no—
752C2×Q8—31no—
753C2×Q8—31no—
754C2×Q8—61no—
755C2×Q8—62no—
756C2×Q8C2×D3211yescharacteristic
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—94no—
760C2×D4—91no—
761C2×D4—91no—
762C2×D4—181no—
763C2×D4—181no—
764C2×D4—182no—
765C2×D4—181no—
766C2×D4—188no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—181no—
770C2×D4—181no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—91no—
779C22×C4—181no—
780C22×C4—182no—
781C22×C4—182no—
782C22×C4—181no—
783C22×C4—181no—
784C22×C4—188no—
785C22×C4—181no—
786Q16—62no—
787Q16—182no—
788SD16—62no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792D8—182no—
793D8—182no—
794M16—62no—
795M16—182no—
796C2×C8—31no—
797C2×C8—31no—
798C2×C8—91no—
799C2×C8C2×D3211yescharacteristic
800C4⋊C4—31no—
801C4⋊C4—61no—
802C4⋊C4—181no—
803C4⋊C4C2×D3211yescharacteristic
804C22⋊C4—61no—
805C22⋊C4—61no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C22⋊C4—181no—
809C42—61no—
810C22×C3—21no—
811C22×C3—32no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—62no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3C2×D3×D411yescharacteristic
821C22×C3C2×D3×D411yescharacteristic
822C2×D3—21no—
823C2×D3—21no—
824C2×D3—21no—
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—22no—
828C2×D3—41no—
829C2×D3—41no—
830C2×D3—62no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—62no—
837C2×D3—61no—
838C2×D3—122no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—124no—
843C2×D3—128no—
844C2×D3—124no—
845C2×D3—128no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—241no—
857C2×D3—241no—
858C2×D3—241no—
859C2×D3—241no—
860C2×D3—241no—
861C2×D3#88212yes—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—21no—
865C3×C4—21no—
866C3×C4—32no—
867C3×C4—42no—
868C3×C4—41no—
869C3×C4—41no—
870C3×C4—61no—
871C3×C4—62no—
872C3×C4—81no—
873C3×C4—121no—
874C3×C4—121no—
875C3×C4C22×D1211yescharacteristic
876C3×C4C2×D3×D411yescharacteristic
877C3×C4C2×D3×D411yescharacteristic
878C3×C4C2×D3×D411yescharacteristic
879Dic3—22no—
880Dic3—21no—
881Dic3—41no—
882Dic3—41no—
883Dic3—61no—
884Dic3—61no—
885Dic3—121no—
886Dic3#88212yes—
887C32#300511yescharacteristic, complemented, Sylow
888C23—31no—
889C23—31no—
890C23—61no—
891C23—91no—
892C23—184no—
893C23—182no—
894C23—181no—
895C23—181no—
896C23—361no—
897C23—361no—
898C23—362no—
899C23—362no—
900Q8—21no—
901Q8—32no—
902Q8—64no—
903Q8—61no—
904Q8—61no—
905Q8—61no—
906Q8D3×D1212yes—
907D4—32no—
908D4—64no—
909D4—61no—
910D4—92no—
911D4—184no—
912D4—184no—
913D4—184no—
914D4—184no—
915D4—181no—
916D4—181no—
917D4—181no—
918D4—362no—
919D4—362no—
920D4—362no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—31no—
924C2×C4—32no—
925C2×C4—32no—
926C2×C4—31no—
927C2×C4—64no—
928C2×C4—64no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—91no—
935C2×C4—184no—
936C2×C4—182no—
937C2×C4—182no—
938C2×C4—184no—
939C2×C4—182no—
940C2×C4—184no—
941C2×C4—181no—
942C2×C4—181no—
943C2×C4—362no—
944C2×C4C22×D3211yescharacteristic
945C8—21no—
946C8—61no—
947C8—61no—
948C8—181no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—62no—
953C2×C3—121no—
954C2×C3—122no—
955C2×C3C2×#88211yescharacteristic
956C2×C3D3×#12011yescharacteristic
957C2×C3#576811yescharacteristic
958C2×C3#577711yescharacteristic
959C2×C3#577711yescharacteristic
960C2×C3#577711yescharacteristic
961D3—22no—
962D3—41no—
963D3—42no—
964D3—121no—
965D3—122no—
966D3—121no—
967D3—122no—
968D3—241no—
969D3—242no—
970D3—241no—
971D3—241no—
972D3—481no—
973C22—32no—
974C22—61no—
975C22—61no—
976C22—61no—
977C22—61no—
978C22—62no—
979C22—61no—
980C22—121no—
981C22—121no—
982C22—181no—
983C22—181no—
984C22—182no—
985C22—181no—
986C22—364no—
987C22—368no—
988C22—361no—
989C22—361no—
990C22—361no—
991C22—361no—
992C22—361no—
993C22D32×D411yescharacteristic
994C4—22no—
995C4—32no—
996C4—41no—
997C4—61no—
998C4—62no—
999C4—121no—
1000C4—121no—
1001C4—181no—
1002C4C2×D3×D1211yescharacteristic
1003C4D32×D411yescharacteristic
1004C3—21no—
1005C3#7895911yescharacteristic, complemented
1006C3#8022711yescharacteristic, complemented
1007C2—62no—
1008C2—121no—
1009C2—122no—
1010C2—361no—
1011C2—362no—
1012C2—721no—
1013C2D3×#88211yescharacteristic
1014C2#1059474611yescharacteristic
1015C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C2×#63948C2semidirect
3. C2×#63794C2semidirect
4. #10594627C2semidirect
5. #10592509C2semidirect
6. C3×#4808C2semidirect
7. C3×#4802C2semidirect
8. #10591602C2semidirect
9. #10591588C2semidirect
10. #10590967C2semidirect
11. #10590961C2semidirect
12. #10590936C2semidirect
13. #10590617C2semidirect
14. #10590616C2semidirect
15. #10590592C2semidirect
32. C2×#3755C22semidirect
33. C2×#3745C22semidirect
34. #64104C22semidirect
35. C2×C3×#216C22semidirect
36. C2×C3×#204C22semidirect
38. C3×#897C22semidirect
42. #63909C22semidirect
46. #63871C22semidirect
47. C2×#3718C22semidirect
48. C2×#3717C22semidirect
49. C2×#3717C22semidirect
50. C2×#3714C22semidirect
53. C32×#103C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#835C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
90. #4808D3semidirect
91. #4802D3semidirect
110. C3×D3×Q8D4semidirect
133. D3×D12D4semidirect
207. C2×#216C2×D3semidirect
226. C2×#204C2×D3semidirect
230. #897C2×D3semidirect
248. C3×#103C2×D3semidirect
249. C3×#103C2×D3semidirect
252. #835C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
263. #816C2×D3semidirect
264. #810C2×D3semidirect
270. #809C2×D3semidirect
392. D3×Q8D12semidirect
577. #103D32semidirect
887. C32#3005semidirect
1005. C3#78959semidirect
1006. C3#80227semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D3×#2392
C2×#639482
C2×#637942
#105946272
#105925092
C3×#48082
C3×#48022
#105916022
#105915882
#105909672
#105909612
#105909362
#105906172
#105906162
#105905922
#802273
#789593